The cochlea of the normal inner ear transforms an input mechanical vibration
(essentially a filtered version of the acoustic signal input to the ear)
to action potentials in the fibres of the auditory nerve. The cochlear
is a rigid, coiled tube, divided mechanically into two along its length
by the basilar membrane. The small bones of the middle ear input a displacement
signal to one side of the tube via a window. This signal drives a transverse
wave in the basilar membrane, whose cutoff frequency decreases along its
length. As a result, high frequencies cause maximum vibration at the window
end, and low frequencies cause maximum vibration at the other.

In the
normal ear, action potentials are produced in an array of hair cells which
reside on the basilar membrane. Ohm [2] and Helmholtz [3] proposed that
pitch was encoded tonotopically, i.e. by the place along the basilar membrane
of the nerve stimulated (place theory), whence the term 'place theory' or 'place pitch'. In contrast Seebeck [4] argued that nerve
pulses were produced by each vibration and that their rate determined
the perceived pitch: 'rate theory' or 'rate pitch'.

In the place theory, it is difficult
to explain the observed fine resolution of frequency (~0.2%). The rate
theory cannot readily explain the perception of tones with frequencies
many times greater than the maximum firing rate of neurones. Despite many
elegant acoustic experiments, the relative importance of rate and place
are still debated because, in the normal ear, the rate of mechanical stimulation
of the basilar membrane is strongly correlated with position. Cochlear
implants allow the local electrical stimulation of different regions of
the cochlea at different rates. A range of experiments have studied pitch
using CIs: Simmons et al [5] reported pitch estimates from a single subject
with low resolution in position. Pitch as a function of stimulation rate
was reported by Pijl [6] and by Collins et al [7].

Our study extends the work by these researchers and uses the method
of pitch scaling [7,8] which has the advantages that it does not require
matching of percepts that may differ in several different perceptual
parameters, and that it can readily be understood and used by subjects
with little knowledge of music. We studied six volunteers with implants
which allowed fine resolution in rate and place, and we present perceived
pitch as a function of rate and place of stimulation. The results show
remarkable consistency, given the subjective nature of the test.

Six adults who had lost their hearing at ages between 5 and 45 years
volunteered for this study, which is part of a project to improve the
performance of CIs in delivering perception and appreciation of music.
The stimuli were 1.00 s pulse trains of biphasic rectangular pulses:
a 100 microsecond pulse, a 25 microsecond gap then a 100 microsecond
pulse in the opposite direction. The stimuli were loudness balanced
by asking each subject first to increase the control of the current
level to achieve a "medium-loud" level, then to compare all stimuli
in turn with the middle rate, middle position stimulus until the subject
was satisfied with loudness equivalence.

Figure 2a shows the result for the experiment over the larger range.
At low frequencies, the pitch is strongly dependent on both rate and
place but, at rates above several hundred pps, the stimulation rate
has little effect and pitch decreases with distance from the round window.

Figure 2. Average of the scaled pitch estimate (plus or minus
s.e.) as a function of stimulation rate and electrode position. Higher
number electrodes are inserted further into the cochlea (most distant
from the window). The different electrode pairs in (b) are displaced
from each other by 0.75 mm. To elicit reports of perceived pitch from
a subjects unfamiliar with the names of musical intervals, the pitch
scaling method [7,8] was used: subjects were asked to rate pitch on
an arbitrary scale from 0 (low pitch) to 100 (high). Seven examples
of each stimulus were delivered and evaluated. Presentation order was
random. For each subject in each of the two experiments, the responses
were scaled as a percentage of the total range used by the subject.
The number, time and good will of volunteers are generous but finite.
This limits the volume of parameter space that may be investigated.
One experiment investigated rates from 100 to 500 pps, applied between
the three pairs of electrodes at the end of the array most distant from
the round window (1b). The positions given are the average values measured
in another study [9]. Five of the subjects returned for another experiment
in which rates between 100 and 1000 pps were applied to three pairs
of electrodes widely spaced along the array (1a). All used Nucleus (TM)
CI22M implants and either SPECTRA-22(TM) or SPrint(TM) processors programmed
with the SPEAKTM coding strategy (Cochlear Ltd.). All subjects normally
use biphasic pulses applied between pairs of electrodes separated by
one temporarily inactive electrode; that stimulation mode was used in
this study.

Figure 2b shows the average of the scaled pitch for all subjects for
the experiment with smaller rate and place range. The difference between
electrodes at 15.5 mm and 16.3 mm is significant at 0.05, which suggests
that the resolution of position in this context is of the order of,
or less than, one electrode spacing (0.75 mm). The logarithmic dependence
of pitch on rate invites comparison with normal hearing, where notes
in the equal tempered chromatic scale of Western music are equally spaced
on a log frequency scale.

For the CI subjects, pitch also depends on place of stimulation, decreasing
with distance from the round window. This can be compared with the tonotopic
arrangement of the normal ear where a doubling in the frequency of the
acoustic signal corresponded to a displacement of about 4 mm along the
basilar membrane for frequencies above several hundred Hz, and smaller
displacements for lower frequencies [10]. Because the pitch scales shown
in Fig 2b are approximately logarithmically dependent on rate, we can
calculate that a doubling in stimulation rate corresponds to a displacement
of about 2 mm in this range. For the series of experiments reported
in Fig 2a, the displacement corresponding to a doubling of stimulation
rate depends on position and rate. It is about 4-6 mm at low rates and
decreases for higher rates. The results for electrodes at 17 mm are
slightly different between the two experiments. This is partly because
the pitch scale is arbitrary and the experiments were conducted at different
times. It is also possible that the task of assigning pitch is more
difficult over a much larger range of the parameters.

The apparent saturation of the dependence of pitch on stimulation
rate is not surprising at rates which are greater than the maximum firing
rate of neurones. These results may not simply be compared with normal
hearing, however, because the differential mechanical stimulation of
hair cells is rather different from the electrical stimulation by the
CI of many or all of the cells between or near the two electrodes. The
influence of rate and place on pitch perception for these post-lingually
deafened subjects nevertheless suggests that both rate and place are
important in pitch coding for normal hearing at low frequencies, but
that place alone dominates at sufficiently high frequencies.

Acknowledgements. RF was supported by an Australian Postgraduate
Award (Industry). We thank Stephanie Shaw and our volunteer subjects.